1. Technical Field of the Invention
The invention relates to a method for eliminating first, second and third-order axial image deformations during correction of the third-order spherical aberration in electron optical systems with hexapoles.
2. Description of the Prior Art
It is generally known that the resolution of circular lenses in electron optical systems is limited by the third-order aberration (spherical aberration). In numerous fields of application, such as electron microscopy, the capacity of an electron optical system is defined by the resolution so that to improve such devices considerable efforts are made to eliminate the third order spherical aberration. One of the most promising solutions is the use of corrective means comprising noncircular lens systems, as for example described in EP 0451370, where a corrective means constituted by circular lenses and hexapoles, in the direction of the optical path, is disposed behind the lens system to be corrected, which is usually the objective lens of the electron microscope. In the case of the above mentioned corrective means, as with all other electron optical systems with correction of the third-order spherical aberration, in practice, adjustment errors occur that among other things impair the resolution, such errors relating primarily to first, second and third-order axial image deformations, the elimination of which is necessary in order to achieve the optimal resolution. The axial image deformations that occur as adjustment errors during correction of the third-order spherical aberration are as follows:
C1 defocusing
A1 first-order axial astigmatism with twofold symmetry
B2 second-order axial coma
A2 second-order astigmatism with threefold symmetry
A3 third-order astigmatism with fourfold symmetry
S3 third-order star aberration with twofold symmetry
It holds for adjustment errors, which are also termed parasitic errors, that their value is of a small magnitude, and in case of ideal adjustment vanishes. The previous methods are characterised therein that the adjustment errors are eliminated successively for every mapping element of the electron optical system and sequentially in the direction of the beam propagation.
On the basis of this state-of-the-art, the invention has the object of creating an adjustment method with the aid of which the elimination of first, second and third-order axial image deformations can be effected.
As a solution, the following correction methods are explained, which put forward a theory by means of which individual second and third-order axial image deformations can be corrected; on the other hand, an adjustment method is specified for eliminating all first as well as second and third-order axial image deformations during correction to eliminate the third-order spherical aberration. The values {overscore (xcex1)} and {overscore (xcex3)} denote the respective complex conjugates. Subsequently, the correction of the individual image deformations are explained in greater detail in conjunction with the description of the adjustment method.
The first step as a prerequisite for eliminating the adjustment error is to determine the values of the respective aberration coefficients. A decisive difference in comparison to methods known in the state-of-the-art consists therein that the image deformations are measured behind the total system, as a rule comprising several lenses, exactly in the image plane so that the deformation is captured only in its entirety and mutual superposition. In order to determine the value of the respective image deformation coefficients, images are recorded with beam paths tilted against the optical axis, where the individual images have differences in the angle of inclination and azimuth of the illumination axis in relation to one another. Here the number of images is so great that the system of equations is at least determined. The evaluation is effected in the manner that a diffractogramm is produced, either in an analogue manner through diffraction or through a Fourier transform in mathematical treatments. From the diffraction patterns, the image deformations C1, A1 can be determined according to a known method. We refer to the contribution from F. Zemlin et al., Ultramicroscopy 3 (1978) 49. The further four complex adjustment aberrations and the real spherical aberration can be determined through a system of equations which is derived from the eikomal (see Zemlin aaO). With the five aforementioned image deformations, especially a system of equations, which comprises nine real equations, is to be derived and solved. In this way, the determination of the aberration coefficients to be eliminated is performed.
In order to eliminate the adjustment errors, steps are to be performed in the order described below.
Influencing and eliminating the defocusing and the first-order axial astigmatism with twofold symmetry are trivial; they are performed by changing the focussing (in case C1) and through superposition of a quadrupolar field (in case A1). After the first-order deformation is eliminated, the second-order deformations are to be corrected next, that is, the axial coma B2 and the axial astigmatism A2 with threefold symmetry, because only then a sufficiently exact determination of the third-order image deformation can be performed and thus its correction.
After the value has been determined in the prescribed way, the correction is performed as described below:
Second-order axial coma B2:
The elimination can be effected by means of a so-called coma stigmator. To that end, in the corrective system, a pair of hexapoles are superpositioned respectively by a quadrupolar field of the same intensity, whereupon the product from the sign of the hexapole field and that of the associated quadrupolar field are antisymmetrical, that is, are opposed to each other. This condition ensures that no first-order astigmatism is generated. The intensity and orientation of these quadrupolar fields is determined by the measured coma.
In order to implement the quadrupolar fields various options are available. This may be achieved in practice by generating an additional quadrupolar field in the hexapoles of the corrective system.
A different possibility of creating the quadrupolar fields can consist therein of effecting a shifting of the optical axis parallel to the axis of the hexapole.
Second-order axial astigmatism with threefold symmetry A2:
Here the correction is achieved through an additional hexapole field whose intensity and direction is likewise defined through the determined aberration coefficient. Implementation is attained through generation of such a hexapole field. A further possibility for generating a field consists in the virtual twisting of the hexapoles of the correction system against one another, whereupon a field with threefold symmetry is also generated. Implementation is achieved through the arrangement of a magnetic circular lens between the two hexapoles or the use of already existing ones. The advantage of this method consists therein that one saves the otherwise necessary path of use of a twelve-pole lens to generate a hexapole field of option size and alignment.
After first and second-order image deformations are now corrected, the values of the third-order image deformations can be determined in the way described above, namely the axial astigmatism A3 with fourfold symmetry and the star aberration S3 with twofold symmetry. The correction of these axial image deformations follows a common and general principle proposed for the first time by the invention. In order to correct the axial image deformation, the same extra-axial image deformation of higher order is used and by shifting or tilting the optical axis made effective until a compensation is achieved. Equality of the image deformation within the meaning of the invention means the same behaviour, that is, the same dependence on complex aperture angle xcex1 and its complex conjugate {overscore (xcex1)}. Thereby the power of the image coordinate xcex3 corresponds to the difference between the order of the extra-axial deformation used for correction and the order of the axial image deformation to be corrected.
In many applications, for instance, for reasons of controllability and accessibility or during correction of the value of smaller deformations, as occur during adjustment, the extra-axial deformation with linear dependency xcex3 is used. With an axial portion, one would have, for example, xcex1n, whereby the associated extra-axial portionxe2x80x94assuming linearityxe2x80x94is then xcex1nxc2x7xcex3. With a third-order axial star deformation there is xcex13, so that the extra-axial and in xcex3 linear star deformation of the fourth-order used for correction is xcex13xcex3. To correct the third-order axial astigmatism {overscore (xcex1)}3 with fourfold symmetry, the fourth-order extra-axial astigmatism is used.
With the corresponding shifting of the optical axis, preferably in the region of the intermediate image, the extra-axial deformation can be influenced so that with corresponding adjustment a mutual compensation is achieved, i.e. elimination of the axial deformation portion, with the aid of the associated extra-axial image deformation within the meaning of the description above. In this way, the star aberration as well as the third-order astigmatism with fourfold symmetry can be eliminated.
The correction of the third-order deformation in the way described influences in principle the lower order deformations.
For this reason, upon termination of the correction procedure for the third-order image deformation, the resulting second and third order deformation must be measured and subsequently (again) corrected in the way described above. Through the use of suitable adjustment elements, it can be achieved that the first and second order are corrected without or only with a minor effect upon the third-order deformation. This is where the methods explained in claims 6-9 are used.